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<b>let </b><font color="Maroon">G</font> be    <a href="incsp_1.html#L1">IncProjStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">P</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">Q</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">R</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">G</font>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:29"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="projpl_1.html#R5" target="_self">is_a_quadrangle</a> 
 <b>and </b><br/><a NAME="E2:29"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="incproj.html#R3">on</a> <font color="Maroon">P</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="incproj.html#R3">on</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="incproj.html#R3">on</a> <font color="Maroon">R</font> )
 ;<br/>

<a NAME="E3:29"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:29"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">Q</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:29"/>
<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">a</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:29"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E7:29"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">R</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E8:29"/>
<font color="Maroon">d</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a> 
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:29"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">d</font>,<font color="Maroon">b</font> <a href="projpl_1.html#NR6" target="_self">is_a_triangle</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E10:29"/><b>then </b>
<font color="Maroon">R</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">P</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E11:29"/>
<font color="Maroon">P</font>,<font color="Maroon">Q</font>,<font color="Maroon">R</font> <a href="incproj.html#R1">are_mutually_different</a> 
 <b>by </b><i>, <a class="ref" href="projpl_1.html#D1" target="_self">Def1</a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a></i>;<br/>


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